Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-10T15:16:07.411Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Generation of Instability Tollmien-Schlichting Waves by Free-Stream Turbulence

Part of: Turbulence Incompressible viscous fluids

Published online by Cambridge University Press:  09 January 2017

Luyu Shen  and
Changgen Lu
Luyu Shen*
Affiliation:
School of Marine Sciences, Nanjing University of Information Science & Technology, Nanjing 210044, China
Changgen Lu*
Affiliation:
School of Marine Sciences, Nanjing University of Information Science & Technology, Nanjing 210044, China
*
*Corresponding author. Email:shenluyu99@foxmail.com (L. Y. Shen), cglu@nuist.edu.cn (C. G. Lu)
*Corresponding author. Email:shenluyu99@foxmail.com (L. Y. Shen), cglu@nuist.edu.cn (C. G. Lu)
Get access

Abstract

The beginning of the transition from the laminar to a turbulent flow is usually the generation of instability Tollmien-Schlichting (T-S) waves in the boundary layer. Previously, most numerical and experimental researches focused on generating instability T-S waves through the external disturbances such as acoustic waves and vortical disturbances interacting with wall roughness or at the leading-edge of flatplate, whereas only a few paid attention to the excitation of the T-S waves directly by free-stream turbulence (FST). In this study, the generating mechanism of the temporal mode T-S waves under free-stream turbulence is investigated by using direct numerical simulation (DNS) and fast Fourier transform. Wave packets superposed by a group of stability, neutral and instability T-S waves are discovered in the boundary layer. In addition, the relation between the amplitude of the imposed free-stream turbulence and the amplitude of the excited T-S wave is also obtained.

Keywords

Free-stream turbulenceTollmien-Schlichting waveboundary layer

MSC classification

Secondary: 76F65: Direct numerical and large eddy simulation of turbulence 76F40: Turbulent boundary layers 76D33: Waves
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 2 , April 2017 , pp. 429 - 438
Copyright
Copyright © Global-Science Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Schubauer, G. B. and Skramstad, H. K., Laminar-boundary-layer oscillations and transition on a flat plate, Technical Report Archive & Image Library, 1948.Google Scholar
[2] Gaster, M., On the generation of spatially growing waves in a boundary layer, J. Fluid. Mech., 22 (1965), pp. 433–441.CrossRefGoogle Scholar
[3] Goldstein, M. E., The evolution of Tollmien-Sclichting waves near a leading edge, J. Fluid. Mech., 127 (1983), pp. 59–81.CrossRefGoogle Scholar
[4] Ruban, A. I., On the generation of Tollmien-Schlichting waves by sound, Fluid. Dynam., 19 (1984), pp. 709–717.Google Scholar
[5] Goldstein, M. E., Scattering of acoustic waves into Tollmien-Schlichting waves by small streamwise variations in surface geometry, J. Fluid. Mech., 154 (1985), pp. 509–529.Google Scholar
[6] Duck, P. W., Ruban, A. I. and Zhikharev, C. N., The generation of Tollmien-Schlichting waves by free-stream turbulence, J. Fluid. Mech., 312 (1996), pp. 341–371.CrossRefGoogle Scholar
[7] Wu, X., On local boundary-layer receptivity to vortical disturbances in the free stream, J. Fluid. Mech., 449 (2001), pp. 373–393.CrossRefGoogle Scholar
[8] Lu, C. G. and Shen, L. Y., Numerical study on boundary-layer receptivity with localized wall blowing/suction, Acta Phys. Sin., 64 (2015), pp. 224702 (in Chinese).Google Scholar
[9] Shen, L. Y. and Lu, C. G., Boundary-layer receptivity under the interaction of free-stream turbulence and localized wall roughness, Appl. Math. Mech., 37 (2016), pp. 349–360.Google Scholar
[10] Shen, L. Y. and Lu, C. G., Local receptivity in the non-parallel boundary layer, Appl. Math. Mech., 37 (2016), pp. 929–940.CrossRefGoogle Scholar
[11] Wiegel, M. and Wlezien, R. W., Acoustic receptivity of laminar boundary layers over wavy walls, AIAA. P., (1993), 93–3280.Google Scholar
[12] Dietz, A. J., Local boundary-layer receptivity to a convected free-stream disturbance, J. Fluid. Mech., 378 (1999), pp. 291–317.Google Scholar
[13] Luo, J. S. and Zhou, H., On the generation of Tollmien-Schlichting waves in the boundary layer of a flat plate by the disturbances in the free stream, P. Roy. Soc. A-Math. Phy., 413 (1987), pp. 351–367.Google Scholar
[14] Wu, X., Generation of Tollmien-Schlichting waves by convecting gusts interacting with sound, J. Fluid. Mech., 397 (1999), pp. 285–316.CrossRefGoogle Scholar
[15] Zhang, Y., Zaki, T. and Sherwin, S. et al., Nonlinear response of a laminar boundary layer to isotropic and spanwise localized free-stream turbulence, 6th AIAA. Theory Fluid. Mech. Con., 2011.CrossRefGoogle Scholar
[16] Shen, L. Y., Lu, C. G., and Wu, W. G. et al., A high-order numerical method to study three-dimensional hydrodynamics in a natural river, Adv. Appl. Math. Mech., 7 (2015), pp. 180–195.Google Scholar
[17] Lu, C., Cao, W. and Zhang, Y. et al., Large eddies induced by local impulse at wall of boundary layer with pressure gradients, Prog. Nat. Sci., 18 (2008), pp. 873–878.Google Scholar
[18] Dietz, A. J., Boundary-layer receptivity to transient convected disturbances, AIAA. J., 36 (1998), pp. 1171–1177.Google Scholar